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In this paper, a new methodology to extract the elasto-plastic properties of lead-free solder materials from an instrumented sharp indentation loading curve has been proposed using dimensional analysis and finite element computation. The nano indenter XP technology is used to test samples of lead-free eutectic SnAgCu solder alloys to obtain a load-displacement curve, which can be used to calculate its hardness, elastic modulus and contact stiffness using the Oliver's method. Then, a group of dimensionless functions Pi (proposed by Dao et al.), that relate the characteristic parameters of indentation load- unloading curves to the mechanical properties obtained from the stress-strain curves, is used to predict the representative strain, the representative stress, strain hardening exponent and yield stress. Finally, according to the obtained parameters of materials, the 2D axial symmetrical element model was adopted to simulate the nanoindentation process by using the ANSYS finite element code. The validity of the new methodology is checked using the agreement of comparing the load-displacement curves of nanoindentation impressions in the experiments with FEM results. Eutectic SnPb solder was also examined for comparative purpose.